Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization
This work addresses the challenge of learning sparse nonlinear dynamics for scientific machine learning, offering a more robust and efficient method compared to existing heuristic approaches, though it is incremental as it builds on the SINDy framework.
The paper tackles the problem of discovering governing equations of complex dynamical systems from data by proposing an exact formulation of the sparse identification of nonlinear dynamics (SINDy) problem using mixed-integer optimization (MIO) to solve sparsity constrained regression to provable optimality in seconds, resulting in dramatic improvements in accurate model discovery with increased sample efficiency, robustness to noise, and flexibility for physical constraints.
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic sparse regression methods, has become a dominant tool for learning parsimonious models. We propose an exact formulation of the SINDy problem using mixed-integer optimization (MIO) to solve the sparsity constrained regression problem to provable optimality in seconds. On a large number of canonical ordinary and partial differential equations, we illustrate the dramatic improvement of our approach in accurate model discovery while being more sample efficient, robust to noise, and flexible in accommodating physical constraints.